Related papers: Relative Calabi-Yau completions

Given a negatively graded Calabi-Yau algebra, we regard it as a DG algebra with vanishing differentials and study its cluster category. We show that this DG algebra is sign-twisted Calabi-Yau, and realize its cluster category as a…

We consider a generalization of Calabi-Yau structures in the context of $\alpha$-Sasakian manifolds. We study deformations of a special class of Legendrian submanifolds and classify invariant contact Calabi-Yau structures on 5-dimensional…

The preprints arXiv:math/0610728 and arXiv:math/0612451 are withdrawn due to a problem with Theorem 2.2 in arXiv:math/0610728. The theorem claims that for certain triangulated categories with finitely many indecomposable objects, the…

In this article we study the extendability of a smooth projective variety by degenerating it to a ribbon. We apply the techniques to study extendability of Calabi-Yau threefolds $X_t$ that are general deformations of Calabi-Yau double…

We show that the $\mathbb{Q}$-descents of the canonical $\mathbb{R}$-variation of Hodge structure of Calabi-Yau type over a tube domain of type $A$ can be realized as sub-variations of Hodge structure of certain $\mathbb{Q}$-variations of…

We consider families ${\cal F}(\Delta)$ consisting of complex $(n-1)$-dimensional projective algebraic compactifications of $\Delta$-regular affine hypersurfaces $Z_f$ defined by Laurent polynomials $f$ with a fixed $n$-dimensional Newton…

Consider a $k$-linear Frobenius category $\mathscr{E}$ with a projective generator such that the corresponding stable category $\mathscr{C}$ is 2-Calabi--Yau, Hom-finite with split idempotents. Let $l,m\in\mathscr{C}$ be maximal rigid…

We study noncompact Calabi-Yau threefolds, their moduli spaces of vector bundles and deformation theory. We present Calabi-Yau threefolds that have infinitely many distinct deformations, constructing them explicitily, and describe the…

The preprints arXiv:math/0610728 and arXiv:math/0612451 are withdrawn due to a problem with Theorem 2.2 in arXiv:math/0610728. The theorem claims that for certain triangulated categories with finitely many indecomposable objects, the…

We prove that the equivalence classes of d-dimensional Calabi-Yau $A_\infty$-categories (dCY category for short) of certain type are in one-to-one correspondence with the gauge equivalence classes of graded quivers with potential.

First, we classify Calabi-Yau threefolds with infinite fundamental group by means of their minimal splitting coverings introduced by Beauville, and deduce that the nef cone is a rational simplicial cone and any rational nef divisor is…

We introduce a class of dg-algebras which generalize the classical Brauer graph algebras. They are constructed from mixed-angulations of surfaces and often admit a (relative) Calabi--Yau structure. We discovered these algebras through two…

We study compactifications of F-theory on certain Calabi--Yau threefolds. We find that $N=2$ dualities of type II/heterotic strings in 4 dimensions get promoted to $N=1$ dualities between heterotic string and F-theory in 6 dimensions. The…

We study aspects of an equivalent relation of the charge completeness in six-dimensional (6D) $\mathcal{N}=(1,0)$ supergravity theory and a standard assumption on the global structure of the gauge group involving F-theory geometry, recently…

Let $d$ be a positive integer. In a previous article we established a bijective correspondence between the following classes of objects, considered up to the appropriate notion of equivalence: differential graded algebras with…

This paper determines the full derived deformation theory of certain smooth rational curves C in Calabi-Yau 3-folds, by determining all higher A_\infty-products in its controlling DG-algebra. This geometric setup includes very general cases…

Our aim in this paper is to prove two results related to the three constructions of cluster categories: as orbit categories, as singularity categories and as cosingularity categories. In the first part of the paper, we prove the universal…

Let $X$ denote the total space of cotangent bundle of projective plane. This is a non-compact Calabi-Yau $4$-fold (also called local Calabi-Yau variety in physics literature). The aim of this paper is to use tilting objects to characterize…

Displays can be thought of as relative versions of Fontaine's notion of strongly divisible lattice from integral $p$-adic Hodge theory. In favourable circumstances, the crystalline cohomology of a smooth projective $R$-scheme $X$ is endowed…

We construct singular quartic double fivefolds whose Kuznetsov component admits a crepant categorical resolution of singularities by a twisted Calabi--Yau threefold. We also construct rational specializations of these fivefolds where such a…